Valerio, Luca
,
De centro gravitatis solidorvm libri tres
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CD, ita eſt EF ad GH; erit ex æquali vt A ad CD,
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ad E ad GH: & conuertendo vt
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CD ad A, ita GH ad E: & per
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mutando CD ad GH, ita A ad E.
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<
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>Rurſus quoniam eſt vt A ad B ita
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E ad F: & vt B ad D, ita F ad H;
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erit ex æquali, vt A ad D ita E ad
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H: ſed vt CD ad A, ita erat GH
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ad E; ex æquali igitur erit vt CD ad
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D ita GH ad H: & permutando vt
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CD ad GH, ita D ad H, & reli
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qua C ad reliquam G: ſed vt CD
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ad GH ita erat A ad E; vt igitur
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A ad C ita erit E ad G. </
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PROPOSITIO II.
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>Si circa datæ hyperboles communem diame
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trum parabola deſcripta illius baſim ita diuidat,
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vt quadratum dimidiæ baſis parabole ad reli
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quum quadrati dimidiæ baſis hyperboles eam
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habeat proportionem, quam tranſuerſum latus
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ad diametrum hyperboles; omnes in hyperbole
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ad diametrum ordinatim applicatas ita ſecabit,
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vt exceſſus, quibus quadrata in hyperbole appli
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catàrum ſuperant quadrata in parabola ex ſectio
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ne applicatarum, inter ſe ſint vt quadrata diame
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tri partium inter applicatas, & verticem inter
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iectarum. </
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<
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>Eſto hyperbole ABC, cuius diameter BD, tranſuer-</
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